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Main Authors: Kofnov, Andrey, Bartocci, Ezio, Bura, Efstathia
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2304.09094
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author Kofnov, Andrey
Bartocci, Ezio
Bura, Efstathia
author_facet Kofnov, Andrey
Bartocci, Ezio
Bura, Efstathia
contents We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of systems that can be represented as probabilistic loops; i.e., algorithms that express and implement non-deterministic processes ranging from robotics to macroeconomics and biology to software and cyber-physical systems. K-series statically approximates the joint and marginal distributions of a vector of continuous random variables updated in a probabilistic non-nested loop with nonlinear assignments given a finite number of moments of the unknown density. Moreover, K-series automatically derives the distribution of the systems' random variables symbolically as a function of the loop iteration. K-series density estimates are accurate, easy and fast to compute. We demonstrate the feasibility and performance of our approach on multiple benchmark examples from the literature.
format Preprint
id arxiv_https___arxiv_org_abs_2304_09094
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Moment-based Density Elicitation with Applications in Probabilistic Loops
Kofnov, Andrey
Bartocci, Ezio
Bura, Efstathia
Methodology
Numerical Analysis
Symbolic Computation
Systems and Control
Applications
62G07, 60E05 (Primary) 60B10 (Secondary)
G.3; I.1.1
We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of systems that can be represented as probabilistic loops; i.e., algorithms that express and implement non-deterministic processes ranging from robotics to macroeconomics and biology to software and cyber-physical systems. K-series statically approximates the joint and marginal distributions of a vector of continuous random variables updated in a probabilistic non-nested loop with nonlinear assignments given a finite number of moments of the unknown density. Moreover, K-series automatically derives the distribution of the systems' random variables symbolically as a function of the loop iteration. K-series density estimates are accurate, easy and fast to compute. We demonstrate the feasibility and performance of our approach on multiple benchmark examples from the literature.
title Moment-based Density Elicitation with Applications in Probabilistic Loops
topic Methodology
Numerical Analysis
Symbolic Computation
Systems and Control
Applications
62G07, 60E05 (Primary) 60B10 (Secondary)
G.3; I.1.1
url https://arxiv.org/abs/2304.09094